3D study of the competitions between shear yielding and crazing for a variable thickness on ductile polymers Shu Guo a,b,c , Dery Torres b,c , Sabine Weygand d , Christian Olagnon a , Rafael Estevez b,c,⇑ a MATEIS, INSA Lyon, 69621, France b Université de Grenoble Alpes, F-38000 Grenoble, France c CNRS UMR 5266, SIMaP, F-38000 Grenoble, France d University of Applied Science, HS Karlsruhe, 76133 Karlsruhe, Germany article info Article history: Received 22 December 2014 Received in revised form 28 July 2015 Accepted 28 August 2015 Available online 9 October 2015 Keywords: Crack tip plasticity Fracture Glassy polymers 3D effects abstract The influence of the thickness in mode I fracture tests is investigated with extensive 3D finite elements calculations. A realistic constitutive law for the bulk is used. Failure by craz- ing is described with a cohesive model. A transition from ductile tearing to fracture by craz- ing is observed with increasing thickness. Ductile tearing takes place for thin samples even if possible crazing is allowed. Crazing takes place for thick samples with a noticeable dif- ference in the load level for craze initiation to that for crack propagation. The consequence on the appropriate geometry for the estimation of the minimum toughness is discussed. Ó 2015 Elsevier Ltd. All rights reserved. 1. Introduction Failure characteristics and toughness estimations of the toughness at the onset of crack propagation are investigated. Polycarbonate is taken as representative of a ductile glassy polymer at room temperature, but also because of its commercial importance in structural application. Its fracture toughness is known to be dependent on a number of factors including the molecular weight, the processing, including ageing time, loading rate and specimen geometry. In the present paper, the influ- ence of the specimen geometry is investigated and in particular that of the thickness, which is the only varied parameter. For thick specimen, fracture in glassy polymers depends on the competition between shear yielding and crazing, which are two rate dependent plastic mechanisms, although at different length scales. Shear yielding corresponds to strain localization in the form of shear bands related to the bulk constitutive law with softening upon yielding followed by hardening at continued deformation. Crazing involves also some plasticity but at the micron scale. A rate dependent description of these two mech- anisms is accounted for by Estevez et al. [14] who showed that the ductile to brittle transition with increasing loading rate can be captured and is related to a reduction in the bulk plasticity prior to failure. Their analysis is performed under the assumption of 2D plane strain conditions which imply an infinitely large thickness. The influence of the specimen thickness is investigated here for a given polycarbonate in terms of molecular weight, processing and ageing time. A unique geometry corresponding to a single edge notch specimen (SENT) subjected to uniaxial tension is considered with a blunt notch R of 0.25 mm. A blunt notch is accounted for as sharp cracks are difficult to machine in PC. It allows for a well defined geometry. The thickness t is varied from t/R = 1 to 16, larger ratios being considered in some cases. Evidences of the influence of the http://dx.doi.org/10.1016/j.engfracmech.2015.08.042 0013-7944/Ó 2015 Elsevier Ltd. All rights reserved. ⇑ Corresponding author at: Université de Grenoble Alpes, F-38000 Grenoble, France. Tel.: +33 (0)476826702. E-mail address: Rafael.Estevez@simap.grenoble-inp.fr (R. Estevez). Engineering Fracture Mechanics 149 (2015) 230–249 Contents lists available at ScienceDirect Engineering Fracture Mechanics journal homepage: www.elsevier.com/locate/engfracmech